An object has a mass of 9 kg. The object's kinetic energy uniformly changes from 54 KJ to 0 KJ over t in [0, 4 s]. What is the average speed of the object?

1 Answer
Narad T.
May 12, 2017

The average speed is =73.03ms^-1

Explanation:

The kinetic energy is

KE=1/2mv^2

mass is =9kg

The initial velocity is =u_1

1/2m u_1^2=54000J

The final velocity is =u_2

1/2m u_2^2=0J

Therefore,

u_1^2=2/9*54000=12000m^2s^-2

and,

u_2^2=2/9*0=0m^2s^-2

The graph of v^2=f(t) is a straight line

The points are (0,12000) and (4,0)

The equation of the line is

v^2-12000=(0-12000)/4t

v^2=-3000t+12000

So,

v=sqrt((-3000t+12000)

We need to calculate the average value of v over t in [0,4]

(4-0)bar v=int_0^4sqrt((-3000t+12000))dt

4 barv=[((-3000t+12000)^(3/2)/(-3/2*3000)]_0^4

=((-3000*4+12000)^(3/2)/(-4500))-((-3000*0+12000)^(3/2)/(-4500))

=12000^(3/2)/4500-0^(3/2)/4500

=292.12

So,

barv=292.12/4=73.03ms^-1

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